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MITOCW | 9: Receptive Fields - Intro to Neural Computation

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MITOCW | 9: Receptive Fields - Intro to Neural Computation MITOCW | 9: Receptive Fields - Intro to Neural Computation MICHALE FEE: So today, we're going to introduce a new topic, which is related to the idea of fine- tuning curves, and that is the notion of receptive fields. So most of you have probably been, at least those of you who've taken 9.01 or 9.00 maybe, have been exposed to the idea of what a receptive field is. The idea is basically that in sensory systems neurons receive input from the sensory periphery, and neurons generally have some kind of sensory stimulus that causes them to spike. And so one of the classic examples of how to find receptive fields comes from the work of Huble and Wiesel. So I'll show you some movies made from early experiments of Huble-Wiesel where they are recording in the visual cortex of the cat. So they place a fine metal electrode into a primary visual cortex, and they present. So then they anesthetize the cat so the cat can't move. They open the eye, and the cat's now looking at a screen that looks like this, where they play a visual stimulus. And they actually did this with essentially a slide projector that they could put a card in front of that had a little hole in it, for example, that allowed a spot of light to project onto the screen. And then they can move that spot of light around while they record from neurons in visual cortex and present different visual stimuli to the retina. So here's what one of those movies looks like. So you're hearing the actual potential of a neuron visual cortex. So you can see the neuron generates lots of spikes when you turn a spot of light on a particular part of the visual field. So they will basically play around with spots of light or bars of light and see where the neuron spikes a light, and then they would draw on the screen-- I think they're going to draw in a moment here-- what they would call the receptive field of the neuron. So you can see that this neuron responds with high firing rate when you turn on a stimulus in that small region there. Notice that the cell also responds when you turn off a stimulus that is right in the area surrounding that small receptor field. So the neuron has parts of its receptive field that respond with increased firing when you apply light, and they also have parts of the receptive field that respond with higher firing rate when you remove light. That was actually a cell, I should have said, that's in the thalamus that projects to visual cortex. So that was a thalamic neuron. Here's what a neuron in cortex might look like. So they started recording in the thalamus. They saw that those neurons responded to spots of light in small parts of the visual field. They were actually recording from neurons in the visual cortex. They got kind of-- they couldn't really figure out what the neurons were doing, and they pulled the slide out of the projector, which made an edge of light moving across the visual field. And the neuron they were recording from at that moment responded robustly when they pulled the slide out. And they realized, oh, maybe it's an edge that the neuron is responding to. And so then they started doing experiments with bars of light. Here's an example. So you can see the neuron responds when you turn a light on in this area here. But is responds when you turn light off in this area here. And so you can see they're marking a symbol for positive responses, positive responses to light on here, and negative responses or increased firing when you turn the light off. So there's different parts of the receptive field that have positive and negative components. But you can see that the general picture here is that the process of finding receptive fields at this early stage was kind of random. You just tried different things and hoped to make the neurons spike. And we're going to come back to this idea of finding receptive fields by trying random things, but in a more systematic way, at the end of the lecture today. So here's what we're going to be talking about. So you can see that Hubel and Wiesel were able to describe that receptive field by finding positive and negative parts and writing symbols down on a screen. We're going to take a more mathematical approach and think about what that means in a quantitative model of how neurons respond to stimuli. And the basic model that we'll be talking about is called an LN model, linear/nonlinear model. And we're going to describe neural responses as a linear filter that acts on the sensory stimulus followed by a nonlinear function that just says neurons can only fire at positive rates. So we're going to have our neurons spike when that filter output is positive, but not when the filter output is negative. And we're going to describe spatial receptive fields as a correlation of the receptive field with the stimulus. And we're also going to talk about the idea of temporal receptive fields, which will be a convolution of a temporal receptive field with the stimulus. So the firing rate will be a convolution of a receptive field with the temporal structure of the stimulus. We're going to then turn to the-- combine these things into the concept of a spatial temporal receptive field that simultaneously describes the spatial sensitivity and the temporal sensitivity of a neuron, as an STRF, as it's called. And we'll talk about the concept of separability. And finally, we're going to talk about the idea of using random noise to try to drive neurons, to drive activity in neurons, and using what's called a spike-triggered average to extract the stimulus that makes a neuron spike. And we're going to use that to compute-- we're going to see how to use that to compute a spatial temporal receptive field in the visual system or a spectral temporal receptive field in the auditory system. So let's start with this. What are spatial and temporal receptive fields? So we just saw how you can think of a region of the visual space that makes a neuron spike when you turn light on or makes a neuron spike when you turn light off. And at the simplest level, you can think of that in the visual system as just a part of the visual field that a neuron will respond to. So if you flash of light over here, the neuron might respond. If you flash of light over here, it won't respond. So there's this region of the visual field where neurons respond, but it's more than just a region. There's actually a pattern of features within that area that will make a neuron spike, and other patterns will keep the neuron from spiking. And so we can think of a neuron as having some spatial filter that has positive parts, and I'll use green throughout my lecture today for positive parts of a receptive field, and negative parts. And this is a classic organization of receptive fields, let's say, in the retina or in the thalamus, where you have an excitatory central part of a receptive field and an inhibitory surround of the receptive field. So we can think of this as a filter that acts on the sensory input. And the better the stimulus overlaps with that filter, the more the neuron will spike. So let's formalize this a little bit into a model. So let's say we have some visual stimulus that is an intensity as a function of position x and y. We have sum filter, G, that filters that stimulus. So we put the stimulus into this filter. This filter, in this case, just looks like, in this case, an excitatory surround in an inhibitory center. That filter has an output, L, which is the response of the filter. Then we have some nonlinearity. So we take the response of the filter, L, we add it to some spontaneous firing rate, and we take the positive part of that sum and call that our firing rate. So that would be a typical output nonlinearity. It's called "a threshold nonlinearity," where if the sum of the filter output and the spontaneous firing rate is greater than 0, then that corresponds to the firing rate of the neuron. So in this case, you can see that as a function of L-- I should have labeled that axis L-- as a function of L, when L is 0, you can see the neuron has some spontaneous firing rate, R naught. And if L is positive, the rate goes up. If L is negative, the rate goes down until the rate hits 0. And then once the neuron stops firing, it can't go negative. So the neuron firing rate stays at 0. And then once you have this firing rate of the neuron, what is it that actually determines whether the neuron will spike? So in most models like this, there is a probabilistic spike generator that is a function of the rate output of this nonlinear output.
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